## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ... |

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Page 104

Ratio is a

Ratio is a

**mutual relation**of**two magnitudes**of the**same**•**kind**to**one another**, in**respect**of**quantity**. ' IV .**Magnitudes**are said to have a ratio to**one another**, when the less can be multiplied so as to exceed the other .### What people are saying - Write a review

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### Common terms and phrases

ABCD AC is equal angle ABC angle ACB angle BAC base base BC bisected centre circle circle ABC circumference common compounded Constr demonstrated describe diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremity fall fore four fourth given straight line greater half join less Let ABC likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular plane produced proportionals PROPOSITION proved Q. E. D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square of AC straight line AC Take taken THEOR.-If third touches the circle triangle ABC wherefore whole

### Popular passages

Page 12 - If two triangles have two sides of the one equal to two sides of the...

Page 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.

Page 143 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.

Page 20 - If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let the two straight lines BD.

Page 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times

Page 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Page 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.

Page 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Page 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.